Speaking to BBC Radio 4′s Today programme this morning, McDonnell said: “If we don’t get a general election, then yes, we will go for a People’s Vote.”

But he added: “If we are going to respect the referendum it will be about the deal.”

“Parliament will decide what will be on that ballot paper,” he said when pressed if EU membership should be included.

His comments suggest in any referendum voters would just be asked what sort of Brexit they wanted - deal or no deal.

Labour MP Chris Leslie said not including the option to stay in the EU would be “utterly ridiculous”.

David Lammy, the Labour MP for Tottenham, said “millions” of people had campaiged for another vote.

“They did not do this to be offered a farcical referendum on No Deal or a Bad Deal. It absolutely must include the right to remain in the EU,” he said.

Len McCluskey, the general secretary of the Unite union, also yesterday said it would be “wrong” to allow any referendum to include the option abandoning Brexit entirely.

Labour’s deep splits over Brexit policy have been on display at its party conference in Liverpool which began on Sunday.

More than 100 constituency parties submitted motions demanding a second referendum and thousands of people joined a march calling for a so-called People’s Vote in order to put pressure on Jeremy Corbyn and the party to change course.

But others in the party warn appearing to oppose Brexit in the face of the 2016 referendum result would damage the party’s fortunes with the millions who voted to leave the EU.

Today party members will debate and vote on a motion agreed late last night that sought to reach a compromise between the two sides.

“If we cannot get a general election, Labour must support all options remaining on the table, including campaigning for a public vote,” the motion states.

It has been dismissed as a “disappointing fudge” by one Labour MP who wanted party members to be given the chance today to explicitly support a second referendum.

The row within Labour over how hard to push for a referendum comes as Theresa May holds a Cabinet meeting in London.

The prime minister is battling to save her Chequers plan for Brexit following last week’s humiliating rebuff by the EU.

She is under intense pressure to change course and seek a simpler, less ambitious deal.

At the same time, leading Brexiteers including David Davis and Boris Johnson will lend their support to an alternative plan for leaving the EU produced by the free market Institute of Economic Affairs think-tank.